Question

the ratio of two sides of a parallelogram is as 3 : 5 and, its perimeter is 48 .find the sides of the parallelogram .​

Answer 1

$\large\underline{ \underline{ \sf \maltese{ \: Question:- }}}$

• The ratio of two sides of a parallelogram is as 3 : 5 and, its perimeter is 48 .find the sides of the parallelogram .

$\large\underline{ \underline{ \sf \maltese{ \: Given:- }}}$

• First Side ( length )= 3x
• Second Side ( breadth ) = 5x
• Perimeter = 48

$\large\underline{ \underline{ \sf \maltese{ \: To \: Find :- }}}$

• The Sides of the Parallelogram.

$\large\underline{ \underline{ \sf \maltese{ \: Solution:- }}}$

$\qquad \quad {:} \longrightarrow \sf{\bf{Perimeter \: = \: 2 \: ( \: Length \: + \: Breadth \: ) }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{48\: = \: 2 \: ( \: 3x \: + \: 5x \: ) }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{48\: = \: 2 \: ( \: 8x \: ) }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{48\: = \: 2 \: \times \: 8x \: }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{48\: = \: 16x \: }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{\: \frac{48}{16} = \: x \: }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{\:\cancel \frac{48}{16} = \: x \: }}$

$\qquad \quad {:} \longrightarrow \sf{\bf{\: 3 = \: x \: }}$

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Sides of Parallelogram :-

• First Side = 3x = 3 × 3 = 9metre
• Second Side = 5x = 5 × 3 = 15metre

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$\large\underline{ \underline{ \sf \maltese{ \: Diagram- }}}$

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 9 cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 15 cm}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

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Answer 2

Step-by-step explanation:

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The ratio of two sides of parallelogram is 3 : 5 and its perimeter is 48 cm.

Let length = l and breadth = b (l >b)

⠀⠀⠀⠀⠀⠀Then b : l = 3 : 5.

$b = \frac{31}{5} \\ \\ perimeter \: = 2(l + b) = 48cm \\ \\ 2(1 + \frac{31}{5} ) = 48cm \\ \\ \\ \frac{81}{5} = 24cm \\ \\ l = 15cm \\ \\ then \: b \: = 9cm$

$\huge \bf{ \boxed{ \boxed{ \red{ \bigstar{ \underline{ \sf{ \blue{ \mathfrak{answer}}}}}}}}}$

⠀⠀⠀⠀⠀⠀The sides are 15 cm, 9 cm,15cm, 9 cm.

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